Related papers: The Network Structure of Mathlib
The Mizar Mathematical Library (MML) is a rich database of formalized mathematical proofs (see http://mizar.org). Owing to its large size (it contains more than 1100 "articles" summing to nearly 2.5 million lines of text, expressing more…
Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be…
Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…
We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion in mathlib, which is a community-driven effort to build a unified mathematics library for Lean. One goal of the mathlib project is to contain all of the topics of…
With the rapid emergence of graph representation learning, the construction of new large-scale datasets is necessary to distinguish model capabilities and accurately assess the strengths and weaknesses of each technique. By carefully…
Large Language Models (LLMs) excel at both informal and formal (e.g. Lean 4) mathematical reasoning but still struggle with autoformalisation, the task of transforming informal into formal mathematical statements. Autoformalisation helps…
Large-scale formalization projects in Lean rely on blueprints: structured dependency graphs linking informal mathematical exposition to formal declarations. While blueprints are central to human collaboration, existing tooling treats the…
Recent progress in large language models has renewed interest in how multi-step reasoning is represented internally. While prior work often treats reasoning as a linear chain, many reasoning problems are more naturally modeled as directed…
We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…
Data leakage has been identified in 648 published machine learning papers across 30 scientific fields. The knowledge to prevent it exists; the tools do not enforce it. This paper presents a grammar - eight typed primitives, a directed…
Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…
Neural networks are increasingly used to support decision-making. To verify their reliability and adaptability, researchers and practitioners have proposed a variety of tools and methods for tasks such as NN code verification, refactoring,…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…
Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic…